RECENT ASSIGNMENT

I need you to create the demand and supply of the labor market and demand and supply of the goods market using the production function and consumption utility function given. Solving the equations and graphing the models have to be through excel and word.
For production function: assume numbers for data for the parameters.
For the consumption function: check past papers estimation of the elasticities to estimate the parameters.
The utility functions will be provided in a word file attached that explains the methodology that you must do.
The effects will be studied in a general equilibrium model by creating a consumption utility function for households and using the Cobb-Douglas production function for firms.
The consumption function comes from the consumer maximizing utility and the production function is the input of the firm’s profit maximization problem. Through the consumer problem, by maximizing the household utility function, subject to the budget constraint, the solution to this problem will give me the labor supply curve and goods demand curve.
(1) U(C,l)=C^(1-?)/(1-?)+l^(1-?)/(1-?)
Here, the household consumption utility function is shown where C denotes consumption and l denotes leisure.
(2) pC+wl=M+wL ¯
Here, the budget constraint is given where C denotes consumption, p denotes price, w denotes wage, l denotes leisure, M denotes non-labor income, and L ¯ denotes total leisure time.
From the goods demand curve after the value added tax, we will be able to analyse whether people in the UAE are demanding less of the goods domestically and we may find that they would substitute the goods elsewhere.
For firms, the producer problem involves maximizing profits. Therefore, we maximize price x output, where output is given from the Cobb Douglas, and subtracting cost of the inputs, capital and labor. This means that solving for profits will give me the goods supply function and labor demand function. After completing the labor and goods markets, the macroeconomic model of the UAE needed for the research would be established and ready to add the changes of the value added tax.

(3) Y=K^a h^(1-a)
Here, output given as a function of capital and labor using the Cobb Douglas production function. K denotes capital and h denotes labor.
(4) Profit=pK^a h^(1-a)-rK-wh
Here, profit is given as revenues (price times output) minus the cost. p denotes price, r denotes rental rate of capital, and w denotes wage.
Once the value added tax is added, the budget constraint for household consumption becomes:
(5) (1-t)pC+wl=M+wL ¯,
where t would be the 5 percent value added tax.
The data for the parameters of the utility function for households will be based on consumer preferences between leisure and labor. Preferences will be inferred from observed people’s behavior like income elasticities which we will take from past papers.